|(Petroglyph 014) N.Roman - The Synesthesic Project (The music) - N.Roman|
Tracklist 1.Black 2.Blue 3.Red 4.Yellow 5.White N.Roman is an experimental and drone producer, born and living in Valladolid (Spain). He is also very involved in netlabelism since 2008, with some EPs released in netlabels (aka Dubkrauz). In fact, he's the curator of Coda Netlabel, a techno netlabel since 2009. N.Roman website Petroglyph Music website September 25. 2012
Keywords: petroglyph-music; N.Roman; The Synesthesic Project (The music); Experimental; Spain
|On the Multimomentum Bundles and the Legendre Maps in Field Theories - A. Echeverria-Enriquez|
We study the geometrical background of the Hamiltonian formalism of first-order Classical Field Theories. In particular, different proposals of multimomentum bundles existing in the usual literature (including their canonical structures) are analyzed and compared. The corresponding Legendre maps are introduced. As a consequence, the definition of regular and almost-regular Lagrangian systems is reviewed and extended from different but equivalent ways.
|Multivector Fields and Connections. Setting Lagrangian Equations in Field Theories - A. Echeverria-Enriquez|
The integrability of multivector fields in a differentiable manifold is studied. Then, given a jet bundle $J^1E\to E\to M$, it is shown that integrable multivector fields in $E$ are equivalent to integrable connections in the bundle $E\to M$ (that is, integrable jet fields in $J^1E$). This result is applied to the particular case of multivector fields in the manifold $J^1E$ and connections in the bundle $J^1E\to M$ (that is, jet fields in the repeated jet bundle $J^1J^1E$), in order to character...
|Pre-multisymplectic constraint algorithm for field theories - M. de Leon|
We present a geometric algorithm for obtaining consistent solutions to systems of partial differential equations, mainly arising from singular covariant first-order classical field theories. This algorithm gives an intrinsic description of all the constraint submanifolds. The field equations are stated geometrically, either representing their solutions by integrable connections or, what is equivalent, by certain kinds of integrable m-vector fields...
|Geometric Hamilton-Jacobi Theory for Nonholonomic Dynamical Systems - J. F. Cariñena|
The geometric formulation of Hamilton--Jacobi theory for systems with nonholonomic constraints is developed, following the ideas of the authors in previous papers. The relation between the solutions of the Hamilton--Jacobi problem with the symplectic structure defined from the Lagrangian function and the constraints is studied. The concept of complete solutions and their relationship with constants of motion, are also studied in detail...
|Mathematical Foundations of Geometric Quantization - A. Echeverria-Enriquez|
In this review the foundations of Geometric Quantization are explained and discussed. In particular, we want to clarify the mathematical aspects related to the geometrical structures involved in this theory: complex line bundles, hermitian connections, real and complex polarizations, metalinear bundles and bundles of densities and half-forms. In addition, we justify all the steps followed in the geometric quantization programme, from the standpoint definition to the structures which are successi...
|Geometric Hamilton-Jacobi Theory - J. F. Carinena|
The Hamilton-Jacobi problem is revisited bearing in mind the consequences arising from a possible bi-Hamiltonian structure. The problem is formulated on the tangent bundle for Lagrangian systems in order to avoid the bias of the existence of a natural symplectic structure on the cotangent bundle. First it is developed for systems described by regular Lagrangians and then extended to systems described by singular Lagrangians with no secondary constraints...
|Skinner-Rusk Unified Formalism for Optimal Control Systems and Applications - M. Barbero-Liñan|
A geometric approach to time-dependent optimal control problems is proposed. This formulation is based on the Skinner and Rusk formalism for Lagrangian and Hamiltonian systems. The corresponding unified formalism developed for optimal control systems allows us to formulate geometrically the necessary conditions given by Pontryagin's Maximum Principle, provided that the differentiability with respect to controls is assumed and the space of controls is open...